(Refer to HW6 #2) Rural and urban students are to be
compared on the basis of their scores on a
nationwide musical aptitude test. Two random sample of sizes 90 and
100 are selected from rural
and urban seventh grade students. The summary statistics from the
test scores are
Rural Urban
Sample size 90 100
Mean 76.4 81.2
Standard deviation 8.2 7.6
Do these data provide strong evidence that there is a difference in
population mean scores between
urban and rural students? Perform the hypothesis testing (at the
significance level α = .01) by
answering the questions arranged in the following.
(a) Define the µ1 and µ2 in the context of the problem.
(b) Formulate the null and alternative hypotheses.
(c) State the test statistic and its distribution.
(d) Determine the critical value for α = .01 and state the decision
rule.
(e) Calculate the observed value of the test statistic from the
data.
(f) State whether H0 is rejected and tell why.
(g) Calculate the P-value and do the hypothesis testing based on
the P-value.
(h) Express the conclusion in the context of the problem, using
common English
(Refer to HW6 #2) Rural and urban students are to be compared on the basis of...
(Refer to HW6 #6) According to a survey, 73 males out of 786 and 43 females out of 943 report that they usually drive 10 or more miles per hour over the speed limit in Kansas City. We are interested in comparing the proportion of male speeders with the proportion of the female speeders. Is the proportion of male speeders higher than the proportion of female speeders? Perform a hypothesis testing at 6% significance level by answering the following questions....
A liberal arts college in New Hampshire implemented an online homework system for their introductory math courses and wanted to know whether or not the system improved test scores. In the Fall semester, homework was completed the old fashioned way – with pencil and paper, checking answers in the back of the book. In the Spring semester, homework was completed online – giving students instant feedback on their work. The results are summarized below. Population standard deviations were used from...
Suppose a sample of 49 paired differences that have been randomly selected from a normally distributed population of paired differences yields a sample mean d¯ =4.2 of and a sample standard deviation of sd = 7.6. (a) Calculate a 95 percent confidence interval for µd = µ1 – µ2. Can we be 95 percent confident that the difference between µ1 and µ2 is greater than 0? (Round your answers to 2 decimal places.) Confidence interval = [ ? , ?...
Suppose a sample of 49 paired differences that have been randomly selected from a normally distributed population of paired differences yields a sample mean d⎯⎯ =4.6d¯ =4.6 of and a sample standard deviation of sd = 7.6. (a) Calculate a 95 percent confidence interval for µd = µ1 – µ2. Can we be 95 percent confident that the difference between µ1 and µ2 is greater than 0? (Round your answers to 2 decimal places.) Confidence interval = [ , ] ;...
Suppose a sample of 49 paired differences that have been randomly selected from a normally distributed population of paired differences yields a sample mean d¯ =5.0d¯ =5.0 of and a sample standard deviation of sd = 7.8. (a) Calculate a 95 percent confidence interval for µd = µ1 – µ2. Can we be 95 percent confident that the difference between µ1 and µ2 is greater than 0? (Round your answers to 2 decimal places.) Confidence interval = [ , ] ;...
An economist believes that the percentage of urban households with internet access is greater than the percentage of rural household with internet access. He obtains a random sample of 800 urban household and finds that 338 of them have internet access. He obtains a random sample of 750 rural households and finals that 292 of them have internet access. Test the economist's claim at the α=0.05levelofsignificance. In hypothesis testing which of the following is not true? -The conclusion is reject...
The null and alternate hypotheses are: H0:µ1≤µ2. H0:µ1>µ2. A random sample of 29 items from the first population showed a mean of 112 and a standard deviation of 9. A sample of 15 items for the second population showed a mean of 97 and a standard deviation of 12. Use the .01 significance level. a. Find the degrees of freedom for unequal variance test b. State the decision rule for .1 significance level c. Compute the value of the test...
5. A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. Men Women µ µ1 µ2 N 11 59 xˉ 97.52°F 97.37°F S 0.85°F 0.71°F a. Test the claim that men have...
Mike thinks that there is a difference in quality of life between rural and urban living. He collects information from obituaries in newspapers from urban and rural towns in Idaho to see if there is a difference in life expectancy. A sample of 20 people from rural towns give a life expectancy of xr¯=83.7xr¯=83.7 years with a standard deviation of sr=8.9sr=8.9 years. A sample of 7 people from larger towns give xu¯=76xu¯=76 years and su=9.26su=9.26 years. Does this provide evidence...
Ann thinks that there is a difference in quality of life between rural and urban living. She collects information from obituaries in newspapers from urban and rural towns in Idaho to see if there is a difference in life expectancy. A sample of 9 people from rural towns give a life expectancy of xr¯=81.7 years with a standard deviation of sr=5.88 years. A sample of 7 people from larger towns give xu¯=74.1 years and su=9.07 years. Does this provide evidence...